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Making a Big Change: Teaching Math Teaching Statistics

Daren StarnesMathematics Department Chair

The Lawrenceville School

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How do you change

MATH STATISTICS

Math Teachers Into Statistics Teachers

−3𝜎 −2𝜎 −1𝜎01𝜎 2𝜎 3𝜎

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The journey begins with...

Repeat Algebra 1?

AP Statistics

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What math teachers like• Computation

For the data set {1, 3, 4, 4, 4, 5, 7, 8, 9}

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What statistics teachers like

• Real dataA group of elementary school children was asked how many pets they have. Here are their responses, arranged from lowest to highest:

1 3 4 4 4 5 7 8 9

How many pets does the typical student in this class have? Justify your answer.

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What math teachers like• Derivations/proofs

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What statistics teachers like• Concepts

– Mean = balance point of distribution

– Standard deviation = typical distance from mean

Value 1 3 4 4 4 5 7 8 9

Deviation -4 -2 -1 -1 -1 0 2 3 4Squared deviation

16 4 1 1 1 0 4 9 16

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What math teachers don’t like

• Too many words

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What statistics teachers like

• The importance of data production– Sampling versus experimentation

• Methods• Principles• Possible sources of bias

– Scope of inference: random sampling vs. random assignment

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What math teachers like• Classical counting and probability

There are 15 male and 10 female pilots in a lottery. If 8 pilots are chosen at random for a captain’s position, find the probability that 5 or more females are selected.

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What statistics teachers like• Using simulations to estimate probabilities

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Finding common ground?Suppose that one percent of the women in a certain region have breast cancer.

• For women who have breast cancer, the probability of a positive mammogram is 0.90.

• For women who don’t have breast cancer, the probability of a positive mammogram is 0.09.

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P(breast cancer given test +)

P(breast cancer given test +)Think of 1,000 women who participate in screening. We expect that 1000(.01) = 10 have breast cancer. Of these, 10(0.90) = 9 will test positive. Of the 990 who do not have cancer, about 990(0.09) = 89 will test positive.

  Have cancer?  

Test result Yes No Total

Positive      

Negative      

Total     1000 10 990

9 89 989/98 = 0.092

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What did it for me?

• APES/Stats– Field study work in forests and streams– Playing the role of data consultant

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The data are trying to tell us a story…

• Son #1: The firefighter– Call response times

• Son #2: The athletic trainer– Flexibility in knees after exercise

• Son #3: The pilot– Hiring discrimination?

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What makes teaching statistics so difficult for math teachers?

• Lack of content knowledge– Haven’t studied some topics recently/at all– Don’t know underlying theory– Aren’t familiar with statistical vocabulary

• Emphasis on interpretation, not computation• How to assess student understanding

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Will Common Core Help?

• Substantial statistics content added in Grades 7-12 standards

• Rich assessment tasks being developed• Will curriculum materials be sufficient?• What about teacher training?

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Helping math teachers make the change

• Don’t suffocate them with study design!• Stress the statistical problem solving process

– Ask questions– Collect data– Analyze data– Interpret results

• Provide resources and support for teachers who want to learn more about statistics

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How do you change

MATH STATISTICS

Math Teachers Into Statistics Teachers

−3𝜎 −2𝜎 −1𝜎01𝜎 2𝜎 3𝜎

The data are trying to tell us a story